The Bosnian beat the Saints goalkeeper with a wind-assisted long ball inside the first minute, and the Pole is keen to move on from the embarrassing incident
Begovic became only the fifth keeper to score a Premier League goal when he found the net in bizarre circumstances just 13 seconds into a 1-1 draw at the Britannia Stadium on Saturday.
A routine clearance was carried by a strong gust of wind and bounced over Boruc to stun players and spectators alike, bet the Bosnia international did not celebrate his goal and explained why after the game.
"It does not make a goalkeeper look good and I did not want to celebrate out of respect for him," Begovic told BBC Sport.
"It's a cool feeling [for me] but it was a fortunate incident. It was a long ball that got caught in the wind and it took a wicked bounce.
"I feel a bit bad for Boruc. It's not nice to be on the receiving end of those things as a goalkeeper."
Jay Rodriguez's subsequent equaliser for Southampton at least spared the blushes of Boruc, who was understandably keen to move on from the incident.
"I don't want to remember it any more," the Pole said. "I blame the wind for that. I'm really sorry for my team-mates and our supporters, but what can I say.
"What happens, happens and I need to bounce back. I promise to get those two points back."
Begovic is now Stoke's joint leading scorer in the league this season, with Mark Hughes' side having mustered just seven goals so far.